On sampling theory associated with the resolvents of singular Sturm-Liouville problems

Author:
M. H. Annaby

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1803-1812

MSC (2000):
Primary 41A05, 34B05, 94A20

DOI:
https://doi.org/10.1090/S0002-9939-02-06727-8

Published electronically:
October 2, 2002

MathSciNet review:
1955268

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the sampling theory associated with resolvents of eigenvalue problems. We introduce sampling representations for integral transforms whose kernels are Green's functions of singular Sturm-Liouville problems provided that the singular points are in the limit-circle situation, extending the results obtained in the regular problems.

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Additional Information

**M. H. Annaby**

Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Address at time of publication:
Department of Mathematics, Arizona State University, P.O. Box 871804, Tempe, Arizona 85287-1804

Email:
mnaby@math-sci.cairo.eun.eg, annaby@math.la.asu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06727-8

Keywords:
Sampling theory,
singular Sturm-Liouville problems,
Green's function,
resolvent kernels,
Legendre and Bessel functions

Received by editor(s):
November 15, 2000

Received by editor(s) in revised form:
January 18, 2002

Published electronically:
October 2, 2002

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2002
American Mathematical Society